document.write( "Question 669520: Using Cramer's rule solve
\n" ); document.write( "2x - y = 4
\n" ); document.write( "3x + y - z = 10
\n" ); document.write( "y + z = 3
\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #416423 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
I'll try to \"draw\" the matrices. Hope you see it.
\n" ); document.write( "The determinant, D, is
\n" ); document.write( "....... 2 -1 0
\n" ); document.write( "....... 3 1 -1
\n" ); document.write( "....... 0 1 1
\n" ); document.write( "Which evaluates to 7. Hope you know how to do this. Here's the arithmetic
\n" ); document.write( "(1) (2*1*1 + (-1)*(-1)*0 + 0*3*1) - (0*1*0 + 2*1*(-1) + 3*(-1)*1) or
\n" ); document.write( "(2) (2 + 0 + 0) - (0 -2 -3) or
\n" ); document.write( "(3) 2 + 5 = 7 or
\n" ); document.write( "(4) D = 7
\n" ); document.write( "To find x, replace the first column of D with the vector, V, of the right side of your system of equations, namely,
\n" ); document.write( "(5) V = (4 10 3)
\n" ); document.write( "The value of x is given by the determinate of that matrix, X, divided by D, where the determinant of X is
\n" ); document.write( "...... 4 -1 0
\n" ); document.write( "...... 10 1 -1
\n" ); document.write( "...... 3 1 1
\n" ); document.write( "Which evalaluates to 21. Use the same arithmetic as in (1) to (3) to get
\n" ); document.write( "(6) X = 21
\n" ); document.write( "Then the value of x is given by
\n" ); document.write( "(7) x = X/D or
\n" ); document.write( "(8) x = 21/7 or
\n" ); document.write( "(9) x = 3
\n" ); document.write( "Now do the same for y and z, except for y we replace the second column of D with V and the third column of D with V to get z.
\n" ); document.write( "You should get
\n" ); document.write( "(10) y = 2 and
\n" ); document.write( "(11) z = 1
\n" ); document.write( "Now place x, y, and z into to your original three equations to check the answers and get
\n" ); document.write( "Is (2*3 - 2 = 4)?
\n" ); document.write( "Is (6 - 2 = 4)?
\n" ); document.write( "Is (4 = 4)? Yes
\n" ); document.write( "Is (3*3 + 2 - 1 = 10)?
\n" ); document.write( "Is (9 + 1 = 10)?
\n" ); document.write( "Is (10 = 10) ? Yes
\n" ); document.write( "Is (2 + 1 = 3)?
\n" ); document.write( "Is (3 = 3)? Yes
\n" ); document.write( "Answer: Using Cramer's rule we calculate the values of x,y,z to be (3,2,1).\r
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